Logic+ 07
Problem A
This logical problem is known as "Einstein's Riddle" and is considered to be quite a difficult logical problem.
We suggest an approach that seems to be lengthy but effective that gradually leads to a solution.
Here is a problem.
There are five houses on a straight line street, each painted in a different color.
In each house lives a person of a different nationality.
These five owners drink certain beverages (all different), smoke certain cigars (all different) and keep certain pets (all different).
Some information is known about this arrangement. This information is below with abbreviations in parenthesis suggested in the beginning of a solution that follows.
A01. (N1|C1) The Brit lives in the red house.
A02. (N2|P1) The Swede keeps dogs as pets.
A03. (N3|D1) The Dane drinks tea.
A04. (C2-C3) The green house is on the left of the white house.
A05. (C2|D2) The green house’s owner drinks coffee.
A06. (S1|P2) The person who smokes Pall Mall rears birds.
A07. (C4|S2) The owner of the yellow house smokes Dunhill.
A08. (H3|D3) The man living in the center house drinks milk.
A09. (N5|H1) The Norwegian lives in the first house.
A10. (S3/P3) The man who smokes blends lives next to the one who keeps cats.
A11. (P4\S2) The man who keeps horses lives next to the man who smokes Dunhill.
A12. (S4|D4) The owner who smokes Blue Master drinks beer.
A13. (N4|S5) The German smokes Prince.
A14. (N5\C5) The Norwegian lives next to the blue house.
A15. (S3\D5) The man who smokes blend has a neighbor who drinks water.
The question is, who owns the fish?
Solution A
First of all, we will represent all the information in a shorter notation for brevity.
Let's number the houses in order they are located on a street (left to right):
H1, H2, H3, H4 and H5
As it is specified, we have people of 5 different nationalities:
N1 = Brit,
N2 = Swede,
N3 = Dane,
N4 = German,
N5 = Norwegian.
There are 5 different colors of the houses:
C1 = Red,
C2 = Green,
C3 = White,
C4 = Yellow,
C5 = Blue.
There are 5 different drinks:
D1 = Tea,
D2 = Coffee,
D3 = Milk,
D4 = Beer,
D5 = Water.
There are 5 different smokes:
S1 = Pall Mall,
S2 = Dunhill,
S3 = Blends,
S4 = Blue Master,
S5 = Prince.
There are 5 different pet animals:
P1 = Dogs,
P2 = Birds,
P3 = Cats,
P4 = Horses,
P5 = Fish.
The following table will represent all the information we know from a problem:
| House#: | H1 | H2 | H3 | H4 | H5 |
| Nation: | |||||
| Color: | |||||
| Drink: | |||||
| Smoke: | |||||
| Pet: |
The following statements can be immediately used to partially fill our table:
A08: The man living in the center house drinks milk.
A09. The Norwegian lives in the first house.
A14. The Norwegian lives next to the blue house.
| House#: | H1 | H2 | H3 | H4 | H5 |
| Nation: | N5 | ||||
| Color: | C5 | ||||
| Drink: | D3 | ||||
| Smoke: | |||||
| Pet: |
Let's concentrate on the color of the house H1.
It cannot be red (C1) because of conditions A01 and A09.
It cannot be green (C2) or white (C3) because then its neighbor is blue (C5) that contradicts condition A04.
Therefore, its color is the only one remaining - yellow (C4).
From this we can use condition A07 (The owner of the yellow house smokes Dunhill) concluding that in this house H1 the person smokes Dunhill (S2).
Furthermore, using A11 (The man who keeps horses lives next to the man who smokes Dunhill), we conclude that in house H2 the owner keeps horses (P4).
| House#: | H1 | H2 | H3 | H4 | H5 |
| Nation: | N5 | ||||
| Color: | C4 | C5 | |||
| Drink: | D3 | ||||
| Smoke: | S2 | ||||
| Pet: | P4 |
Let's analyse the drink that Norwegian (N5) is drinking in yellow (C4) house H1, smoking Dunhill (S2).
It cannot be milk (D3) because it is drunk in house H3, as we have already determined.
It cannot be tea (D1) because of condition A03 (The Dane drinks tea).
It cannot be coffee (D2) because of condition A05 (The green house’s owner drinks coffee).
It cannot be beer (D4) because of condition A12 (The owner who smokes Blue Master drinks beer).
The only choice of a drink for house H1 is water (D5). Furthermore, this consideration helps to determine the smoke in the house H2 because of condition A15 (The man who smokes blend has a neighbor who drinks water). The smoke in house H2 must be blend (S3).
| House#: | H1 | H2 | H3 | H4 | H5 |
| Nation: | N5 | ||||
| Color: | C4 | C5 | |||
| Drink: | D5 | D3 | |||
| Smoke: | S2 | S3 | |||
| Pet: | P4 |
Now we can determine the nationality of a person in house H2.
It's not Norwegian (N5), who we know lives in house H1.
It's not Brit (N1), who lives in a red (C1) house, as specified in condition A01 (The Brit lives in the red house), while house H2, as we determined, is blue (C5).
It's not Swede (N2) because of condition A02 (The Swede keeps dogs as pets), while we know the pets in house H2 are horses (P4).
It's not German (N4) because of condition A13 (The German smokes Prince), while we know that in house H2 the owner smokes blends (S3).
Therefore, the owner of house H2 must be Dane (N3).
Immediately follows from this is that the drink in house H2 is tea (D1) because of condition A03 (The Dane drinks tea).
| House#: | H1 | H2 | H3 | H4 | H5 |
| Nation: | N5 | N3 | |||
| Color: | C4 | C5 | |||
| Drink: | D5 | D1 | D3 | ||
| Smoke: | S2 | S3 | |||
| Pet: | P4 |
From conditions A04 (The green house is on the left of the white house) follows that a pair of houses green () and white () are either at places H3 and H4 or H4 and H5.
But condition A05 (The green house’s owner drinks coffee) makes the combination H3 and H4 impossible, since we have determined that in house H3 the drink is milk (D3), not coffee (D2). Therefore, the house H4 is green (C2) and H5 is white (C3), which leaves house H3 to be red (C1) and its owner to be Brit (N1) because of the condition A01 (The Brit lives in the red house).
Also, condition A05 (The green house’s owner drinks coffee) tells us that in house H4 the drink is coffee (D2).
That leaves a drink of house H5 to be beer (D4).
From condition A12 (The owner who smokes Blue Master drinks beer) immediately follows that the owner of house H5, where a drink is beer (D4), smokes Blue Master (S4).
| House#: | H1 | H2 | H3 | H4 | H5 |
| Nation: | N5 | N3 | N1 | ||
| Color: | C4 | C5 | C1 | C2 | C3 |
| Drink: | D5 | D1 | D3 | D2 | D4 |
| Smoke: | S2 | S3 | S4 | ||
| Pet: | P4 |
From condition A13 (The German smokes Prince) follows that house H5 cannot belong to German (N4) because the smoke in house H5 is Blue Master (S4), as has been established.
Therefore, the owner of house H5 is Swede (N2) and German (N4) owns house H4.
From condition A02 (The Swede keeps dogs as pets) now follows that pets of house H5 are dogs (P1) and smoke of house H4 is Prince (S5).
That leave smoke Pall Mall (S1) for house H3.
Follows from it and condition A06 (The person who smokes Pall Mall rears birds) that birds (P2) are kept at house H3
| House#: | H1 | H2 | H3 | H4 | H5 |
| Nation: | N5 | N3 | N1 | N4 | N2 |
| Color: | C4 | C5 | C1 | C2 | C3 |
| Drink: | D5 | D1 | D3 | D2 | D4 |
| Smoke: | S2 | S3 | S1 | S5 | S4 |
| Pet: | P4 | P2 | P1 |
From condition A10 (The man who smokes blends lives next to the one who keeps cats) and the established fact that blend (S3) is smoked in house H2 follows that cats (P3) can be in a neighboring to H2 house, either H1 or H3.
But we have already established that birds (P2) are kept at house H3. Therefore, cats (P3) are kept at house H1.
That leaves house H4 for fish (P5).
| House#: | H1 | H2 | H3 | H4 | H5 |
| Nation: | N5 | N3 | N1 | N4 | N2 |
| Color: | C4 | C5 | C1 | C2 | C3 |
| Drink: | D5 | D1 | D3 | D2 | D4 |
| Smoke: | S2 | S3 | S1 | S5 | S4 |
| Pet: | P3 | P4 | P2 | P5 | P1 |
Answer
Fish is kept in house H4 owned by German, painted in green, who drinks coffee and smokes Prince.
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